The Wigner-function approach to quantum transport in mesoscopic electron devices is presented. The concept of Wigner paths allows the formulation of a Monte Carlo simulation which is quantum mechanically rigorous and yet very similar to the one used in semi-classical transport theory. The effect of a potential profile is separated into a term acting as a classical force in the particle orbits and a scattering integral that contains only quantum effects. Phonon scattering is included in the paths in a way that takes automatically into account all quantum effects, such as intracollisional field effect and collisional broadening.